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√y^2=√1
Do i write down both 1 and -1?
The topic is Systems of Non-Linear Equations
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Are you asking:

specifically for √1 which is defined to be the positive square root, so takes just one value, which is 1,

or are you solving y^2 = 1, in which case y could be either of the square roots of 1, which are +/-√1, ie y could be 1 or -1

?
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sqrt(1) is defined as 1.
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1. Sqrt(1) refers to the unique non-negative number that squares to give 1. This is 1.
2. There are two solutions to the equation you give though, which are -1 and 1.
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